Geodesic
The double sum method for Gaussian fields with a parameter set in $l^p$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 4, pp. 1117-1141

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In the paper it is presented a method to compute asymptotics of the probability $\mathsf P\Bigl\{\,\sup\limits_{t\in T}X(t)>u\Bigr\}$, where $X(t)$ is a Gaussian random field with a compact parameter set in the space $l^p$, $1$. On the basis of obtained result it is found the exact asymptotics of tail distribution for the supremum of $l^q$-norm of $l^q$-valued Ornstein–Uhlenbeck process when $q>2$. 
@article{FPM_1996_2_4_a10,
     author = {V. R. Fatalov},
     title = {The double sum method for {Gaussian} fields with a parameter set in $l^p$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1117--1141},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_4_a10/}
}
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V. R. Fatalov. The double sum method for Gaussian fields with a parameter set in $l^p$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 4, pp. 1117-1141. http://geodesic.mathdoc.fr/item/FPM_1996_2_4_a10/